%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:40:38 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 71 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 22 |; 20 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
( doDivides0(xl,xn)
& ? [W0] :
( xn = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) )
& doDivides0(xl,xm)
& ? [W0] :
( xm = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
( doDivides0(xl,sdtpldt0(xm,xn))
| ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ? [W0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,W0)
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f44,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f65,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f66,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f133,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f136,plain,
( doDivides0(xl,xn)
& xn = sdtasdt0(xl,sK3_skl)
& aNaturalNumber0(sK3_skl)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2_skl)
& aNaturalNumber0(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W0,sK2_skl),skolemize(W0,sK3_skl)],[f34]) ).
fof(f137,plain,
aNaturalNumber0(sK2_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
xm = sdtasdt0(xl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f140,plain,
aNaturalNumber0(sK3_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
xn = sdtasdt0(xl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f149,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
& ! [W0] :
( sdtpldt0(xm,xn) != sdtasdt0(xl,W0)
| ~ aNaturalNumber0(W0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f150,plain,
! [X0] :
( sdtpldt0(xm,xn) != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f186,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(sK2_skl,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2_skl)
| ~ aNaturalNumber0(xl) ),
inference(paramodulation,[status(thm)],[f138,f66]) ).
fof(f190,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(sK2_skl,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f133]) ).
fof(f291,plain,
! [X0] :
( sdtasdt0(xl,sdtpldt0(sK2_skl,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f137]) ).
fof(f292,plain,
( sdtasdt0(xl,sdtpldt0(sK2_skl,sK3_skl)) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sK3_skl) ),
inference(paramodulation,[status(thm)],[f141,f291]) ).
fof(f294,plain,
sdtasdt0(xl,sdtpldt0(sK2_skl,sK3_skl)) = sdtpldt0(xm,xn),
inference(forward_subsumption_resolution,[status(thm)],[f292,f140]) ).
fof(f416,plain,
~ aNaturalNumber0(sdtpldt0(sK2_skl,sK3_skl)),
inference(resolution,[status(thm)],[f294,f150]) ).
fof(f449,plain,
( ~ aNaturalNumber0(sK3_skl)
| ~ aNaturalNumber0(sK2_skl) ),
inference(resolution,[status(thm)],[f416,f45]) ).
fof(f450,plain,
~ aNaturalNumber0(sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f449,f137]) ).
fof(f451,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f450,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:32:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.44 % Refutation found
% 0.12/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.45 % Elapsed time: 0.094690 seconds
% 0.12/0.45 % CPU time: 0.411823 seconds
% 0.12/0.45 % Total memory used: 109.516 MB
% 0.12/0.45 % Net memory used: 108.975 MB
%------------------------------------------------------------------------------